3 Answers

Starting in Generation VI, the Poké Ball of the female Pokémon (other than a Master Ball and Cherish Ball, which result in the default standard Poké Ball) will be passed down to its offspring. Male and genderless Pokémon (including Ditto) have no impact on the type of Poké Ball inherited; as such, when breeding a male or genderless Pokémon with Ditto (which is the only way to breed certain species), the offspring is always obtained in a standard Poké Ball.

No
In Gen6 Eggs/baby pkmn inherit the Poke ball from its mother. So we say I catch a Ditto with a Ultra Ball and breed it with with a gastly it turns out a egg with ultra ball. And egg can get pokerus if you have a Pokemon with pokerus in your team.